Kātyāyana's views on the sentence-meaning connection tended towards naturalism. Kātyāyana believed, that the word-meaning relationship was not a result of human convention. For Kātyāyana, word-meaning relations were siddha, given to us, eternal. Though the object a word is referring to is non-eternal, the substance of its meaning, like a lump of gold used to make different ornaments, remains undistorted, and is therefore permanent.

Realizing that each word represented a categorization, he came up with the following conundrum (following Bimal Krishna Matilal):

"If the 'basis' for the use of the word 'cow' is cowhood (a universal) what would be the 'basis' for the use of the word 'cowhood'?

Clearly, this leads to infinite regress. Kātyāyana's solution to this was to restrict the universal category to that of the word itself — the basis for the use of any word is to be the very same word-universal itself."

This view may have been the nucleus of the Sphoṭa doctrine enunciated by Bhartṛhari in the 5th century, in which he elaborates the word-universal as the superposition of two structures — the meaning-universal or the semantic structure (artha-jāti) is superposed on the sound-universal or the phonological structure (śabda-jāti).

In the tradition of scholars like Pingala, Kātyāyana was also interested in mathematics. Here his text on the sulvasutras dealt with geometry, and extended the treatment of the Pythagorean theorem as first presented in 800 BCE by Baudhayana.[2]